Three-dimensional imaging is a well-established method in the diagnosis of diseases of the airway, the colon and the arterial System. In conjunction with fiberoptic methods and computed tomography (CT) three-dimensional imaging and reconstruction has proved to be useful in detection of tumors, obstructions, strictures and certain inflammatory lesions. Virtual endoscopy is a new method of displaying three-dimensional reconstruction of hollow anatomic structures that simulate conventional endoscopy. In contrast to conventional endoscopy, virtual endoscopy is completely noninvasive. Three approaches have been taken: (1) the analysis of local differential geometry features, to automatically detect and assess masses of the airways, and the detection of colonic cancers and polyps, and (2) an analysis of local surface roughness, using fractal dimension calculations, and more recently (3) the use for conformal mapping techniques to project the entire colon surface onto a 2D image. Concerning (1), a variety of local curvature measures have been introduced and applied to both patient and artificial data reconstructions. These functions derive mainly from the estimated values of the principal curvatures (mean and Gaussian curvature local sphericity) and automated detection schemes have been studied that invoke filter sets derived from the local geometry. We continue to work at improving sensitivity and specificity, now using a new, large patient data set, part of an on-going clinical trial at the Mayo clinic. Concerning (2), surface roughness is an important indication of anatomic structural abnormalities and is potentially detectable on virtual endoscopy. Local fractal dimension can be used to quantify surface roughness, such as arterial plaque, and has now been applied to virtual angioscopy to distinguish the thoracic aorta in a normal control from that of a patient predisposed to atherosclerosis. Concerning (3), we recently introduced conformal mapping (angle preserving) techniques from complex analysis to smoothly map the entire colon surface onto a plane representation. This is expected to aid in navigating the colon images, and to better place detected polyps in anatomical context, as locally polpy areas are preserved as well. [1] Summers, Johnson, Pusanik, Malley et al. Automated polyp detection for CT colonography: Feasibility Study. Radiology, 2000, 284-290.[2] Summers, Pusanik, Malley and Hoeg. Fractal analysis of virtual endoscopy reconstructions. Submitted to IEEE Transaction on Medical Imaging, 2000.